Shrimp is very common in New Orleans being a Gulf state. I don't know how this dish came to be known as barbecued shrimp since there is no grilling or smoking.
I've tried different version of the dish. Some restaurants cooked shrimp in a Worcestershire sauce braise while other restaurants used lemon, garlic and a butter sauce. However, the Worcestershire flavored version is the most common.
1/2 lb Shrimp, shell-on, deveined.
1/2 Onion, Chopped
4 T Butter
1/4 t Thyme
1/2 t Ground Black Pepper
2 Clove Garlic, grated
1/4 C Italian Dressing
2T Worcestershire Sauce
1. Shrimp sprinkled with Cajun seasoning and set aside.
The other ingredients....
Saute the onions, garlic and herbs in 2T butter until soft.
Add the shrimp and the liquids (Italian dressing and Worcestershire sauce)... Cook about 10 - 15 minutes.
Add the remaining 2T of butter a little at a time to form a sauce.
The finished dish... usually served with French bread to sop up the sauce.
The flavor was good. I should have added lemon to the dish, even better the next day after the flavors soaked into the shrimp.